A von Neumann algebraic approach to self-similar group actions
Operator Algebras
2020-02-04 v3
Abstract
We study some relations between self-similar group actions and operator algebras. We consider KMS states on the Cuntz--Pimsner algebras constructed by Nekrashevych from self-similar actions and the GNS representations of the KMS states. The KMS states are given by the Bernoulli measure. We also consider the von Neumann algebras on the GNS spaces and show that the von Neumann algebras are type III factors.
Keywords
Cite
@article{arxiv.1905.03986,
title = {A von Neumann algebraic approach to self-similar group actions},
author = {Keisuke Yoshida},
journal= {arXiv preprint arXiv:1905.03986},
year = {2020}
}
Comments
13 pages, to appear in International Journal of Mathematics